Question

In a convex hexagon, prove that sum of all interior angles is equal to twice the sum of its exterior angles formed by producing the sides in the same order.

Answer 1

In a hexagon number of sides$=6$

$\therefore$ Sum of interior angles of a hexagon$=(2\times 6-4)\times 90°=8\times 90°=720°$

Sum of exterior angle of a hexagon $=360°$

$2$ times the sum of exterior angles of hexagon $=2\times 360=720$

From $\left(1\right)\&\left(2\right)$

In a convex hexagon the sum of all interior angle is equal to twice of exterior angles.